新冠肺炎疫情的爆發對傳統教育模式構成了巨大挑戰，進而推動了數位學習(E-Learning)的興起。在這一背景下，知識追蹤技術(Knowledge Tracing: KT)因其協助數位學習發展的有效性而備受關注。本篇論文對注意力知識追蹤(Attentive Knowledge Tracing: AKT)模型實施架構上的改良，特別關注輸入特徵與預測特徵的選澤及特徵融合的架構。此外，我們還擴展了該模型的應用，實現了數學概念分類的可視化，以幫助數學教師驗證數學概念的分類。
同時，本篇論文對教育部因材網以及均一教育平台這兩大線上教育平台進行綜合分析，並在發現大型語言模型(Large Language Model: LLM)於認知和理解方面上的優勢後，深入探討了其在教育領域中的應用。最終，本篇論文使用基於生成型預訓練變換模型4(Generative Pre-trained Transformer 4: GPT-4)的聊天型生成式預訓練轉換器(Chat Generative Pre-trained Transformer: ChatGPT)此聊天機器人，設計了專為國小數學補救的家庭教師系統。此系統能採用蘇格拉底提問的方式幫助學生深入理解知識，還能在結合AKT模型後，提供多樣化的題型，滿足不同程度的學生需求。
本篇論文的綜合分析以及開發的國小數學補救家庭教師系統展示了知識追蹤技術和大型語言模型在教育領域中的潛在價值，為數位學習和教育創新提供了有力的支持。

The outbreak of the COVID-19 pandemic has presented significant challenges to traditional education, prompting the emergence of E-Learning. In this context, Knowledge Tracing (KT) technology has garnered considerable attention for its effectiveness in supporting E-Learning. This paper focuses on architectural improvements to the Attentive Knowledge Tracing (AKT) model, with particular emphasis on the selection of input features and prediction features and the architecture for feature fusion. Furthermore, our research have extended the model's applications to achieve visualizations of mathematical concept classifications, aiding mathematics teachers in verifying the classification of mathematical concepts.
Simultaneously, this paper provides a comprehensive analysis of two major online education platforms in Taiwan, and after discovering the advantages of large language models (LLMs) in terms of cognition and understanding, the applications of LLMs in the field of education are discussed in depth. Ultimately, the paper utilizes a chatbot based on the Generative Pre-trained Transformer 4 (GPT-4) model, known as Chat Generative Pre-trained Transformer (ChatGPT), to design a tutoring system specialized for the field of primary school mathematics remedy. This system assists students in deepening their understanding of knowledge through Socratic questioning. When combined with the AKT model, the system offers a variety of question types to cater to the varied needs of students.
The comprehensive analysis and the development of the primary school mathematics remedial tutoring system in this paper demonstrate the potential value of KT technology and LLMs in the field of education, providing robust support for E-learning and educational innovation.

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